A Logical Measure of Progress for Planning (Technical Report)

Heuristic search planners are so far the most successful. Almost all use as their heuristic an estimate of the distance to a goal state. We formalize a logical measure of progress, defined as a predicate P (x̄, s) true of objects x̄ at a situation s. Actions which increase P ’s extension are guaranteed to move closer to a goal situation, so that P enables us to form plans without search. One example of a measure of progress is the concept of final position used in BlocksWorld. It is not clear how to find a P for an arbitrary domain, so instead we identify three different classes of domains and conditions which allow us to construct a measure of progress. An obvious P will not deliver optimal plans, but it should encode plans which are “good enough.” Our paradigm is entirely within first-order logic, allowing us to extend our results to concurrent domains and those containing non-trivial state constraints. It turns out P not only encodes goal orderings, but subgoal orderings. P also gives rise to a strategy function a(s) which can be used to create a universal (complete) teleo-reactive (TR) program. Given the fact that P -increasing actions will never require backtracking, this TR program can be a powerful on-line planner.